The relationship between the two companies began when the billionaire investor bought an initial stake in the Washington Post company for around $10 million in 1973, a couple of years after it went public.

Mr. Buffett became a close personal friend of Katharine Graham, helping her gain financial acumen during her nearly 30-year run at the paper, bought by her father in 1933.

Ms. Graham’s son Don Graham, who runs the company, is also a friend of Mr. Buffett’s, and is known to seek the Omaha investor’s counsel, including when deciding to sell the Washington Post last year to Amazon.com chief Jeff Bezos for $250 million.

No doubt the two men will remain friends, but the current business relationship looks like it might end if the ongoing discussions, disclosed in a regulatory filing yesterday, result in a deal.

The talks appear to be another example of Mr. Buffett using his ownership of a company’s shares as a pathway to some clever deal-making.

Any deal would have Graham Holdings transfer some of its assets and potentially, Berkshire shares that it owns, into an as-yet unformed subsidiary company. Berkshire would then acquire this subsidiary, using its 1.73 million Graham shares to pay for it.

Such a transaction is called a “tax-free split-off” and companies with long-term ties to each other often explore that option – not just because it’s tax-efficient but also because it’s a mutually beneficial way to sever a relationship without things getting messy.

Tax experts say the IRS considers such transactions as restructurings, rather than sales, of assets and therefore not taxable as long as they pass certain tests.

Given that Berkshire’s 28% stake in Graham is worth about $1.1 billion at yesterday’s closing price, the subsidiary entity would likely have to have assets and stock adding up to that much in value.

Those assets could be any mix of businesses Graham Holdings has in its portfolio. Graham owned about $229 million of Berkshire Hathaway stock through its defined benefit pension plan as of the end of the third quarter, according to the company. As of the end of 2012, the company also owned $335 million of Berkshire stock as part of an investment portfolio.

Graham Holdings used to be known as The Washington Post Co. but renamed itself in November after selling its flagship paper.

Now, the company, which has a market capitalization of roughly $5 billion, owns Kaplan, the educational services provider, six local television stations that reach about 8% of U.S. households and Cable ONE, a Phoenix-based cable operator in 19 states.

It also owns online news site Slate.com, SocialCode, a social marketing company; Celtic Healthcare, a hospice services provider and Forney, an industrial applications company. As of the third quarter of 2013, Kaplan accounted for the biggest chunk of revenue at $546 million, followed by cable and television broadcasting.

Berkshire doesn’t own television or cable companies outright, but stakes in several media companies are part of its massive stock portfolio. That includes satellite operators DirecTV and Dish Network, cable channel Starz, Liberty Media and Viacom. Buying Graham Holdings’ cable assets therefore might not be a stretch, given that cable operators throw off steady cash flow – the kind of business Mr. Buffett likes.